Reusable fuzzy extractors for low-entropy distributions

Ran Canetti, Benjamin Fuller, Omer Paneth, Leonid Reyzin, Adam Davison Smith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

23 Citations (Scopus)

Abstract

Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a secret into the same uniformly distributed key. To eliminate noise, they require an initial enrollment phase that takes the first noisy reading of the secret and produces a nonsecret helper string to be used in subsequent readings. Reusable fuzzy extractors (Boyen, CCS 2004) remain secure even when this initial enrollment phase is repeated multiple times with noisy versions of the same secret, producing multiple helper strings (for example, when a single person’s biometric is enrolled with multiple unrelated organizations). We construct the first reusable fuzzy extractor that makes no assumptions about how multiple readings of the source are correlated (the only prior construction assumed a very specific, unrealistic class of correlations). The extractor works for binary strings with Hamming noise; it achieves computational security under assumptions on the security of hash functions or in the random oracle model. It is simple and efficient and tolerates near-linear error rates. Our reusable extractor is secure for source distributions of linear min-entropy rate. The construction is also secure for sources with much lower entropy rates—lower than those supported by prior (nonreusable) constructions—assuming that the distribution has some additional structure, namely, that random subsequences of the source have sufficient minentropy. We show that such structural assumptions are necessary to support low entropy rates. We then explore further how different structural properties of a noisy source can be used to construct fuzzy extractors when the error rates are high, building a computationally secure and an information-theoretically secure construction for large-alphabet sources.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
EditorsJean-Sebastien Coron, Marc Fischlin
PublisherSpringer Verlag
Pages117-146
Number of pages30
ISBN (Print)9783662498897
DOIs
StatePublished - Jan 1 2016
Event35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016 - Vienna, Austria
Duration: May 8 2016May 12 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9665
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016
CountryAustria
CityVienna
Period5/8/165/12/16

Fingerprint

Extractor
Entropy
Hash functions
Strings
Biometrics
Error Rate
Structural properties
Random Oracle Model
Hash Function
Subsequence
Structural Properties
Convert
Person
Eliminate
Binary
Sufficient
Necessary

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Canetti, R., Fuller, B., Paneth, O., Reyzin, L., & Smith, A. D. (2016). Reusable fuzzy extractors for low-entropy distributions. In J-S. Coron, & M. Fischlin (Eds.), Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings (pp. 117-146). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9665). Springer Verlag. https://doi.org/10.1007/978-3-662-49890-3_5
Canetti, Ran ; Fuller, Benjamin ; Paneth, Omer ; Reyzin, Leonid ; Smith, Adam Davison. / Reusable fuzzy extractors for low-entropy distributions. Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. editor / Jean-Sebastien Coron ; Marc Fischlin. Springer Verlag, 2016. pp. 117-146 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Canetti, R, Fuller, B, Paneth, O, Reyzin, L & Smith, AD 2016, Reusable fuzzy extractors for low-entropy distributions. in J-S Coron & M Fischlin (eds), Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9665, Springer Verlag, pp. 117-146, 35th Annual International Conference on Theory and Applications of Cryptographic Techniques, EUROCRYPT 2016, Vienna, Austria, 5/8/16. https://doi.org/10.1007/978-3-662-49890-3_5

Reusable fuzzy extractors for low-entropy distributions. / Canetti, Ran; Fuller, Benjamin; Paneth, Omer; Reyzin, Leonid; Smith, Adam Davison.

Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. ed. / Jean-Sebastien Coron; Marc Fischlin. Springer Verlag, 2016. p. 117-146 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9665).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a secret into the same uniformly distributed key. To eliminate noise, they require an initial enrollment phase that takes the first noisy reading of the secret and produces a nonsecret helper string to be used in subsequent readings. Reusable fuzzy extractors (Boyen, CCS 2004) remain secure even when this initial enrollment phase is repeated multiple times with noisy versions of the same secret, producing multiple helper strings (for example, when a single person’s biometric is enrolled with multiple unrelated organizations). We construct the first reusable fuzzy extractor that makes no assumptions about how multiple readings of the source are correlated (the only prior construction assumed a very specific, unrealistic class of correlations). The extractor works for binary strings with Hamming noise; it achieves computational security under assumptions on the security of hash functions or in the random oracle model. It is simple and efficient and tolerates near-linear error rates. Our reusable extractor is secure for source distributions of linear min-entropy rate. The construction is also secure for sources with much lower entropy rates—lower than those supported by prior (nonreusable) constructions—assuming that the distribution has some additional structure, namely, that random subsequences of the source have sufficient minentropy. We show that such structural assumptions are necessary to support low entropy rates. We then explore further how different structural properties of a noisy source can be used to construct fuzzy extractors when the error rates are high, building a computationally secure and an information-theoretically secure construction for large-alphabet sources.

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Canetti R, Fuller B, Paneth O, Reyzin L, Smith AD. Reusable fuzzy extractors for low-entropy distributions. In Coron J-S, Fischlin M, editors, Advances in Cryptology - EUROCRYPT 2016 - 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Springer Verlag. 2016. p. 117-146. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-662-49890-3_5